Set is haysta

set Compact waa meel topological qeexay in cover taas oo subcover uguna. meelaha Compact in topology ee guryaha ay u eg waxaa laga yaabaa in hab kooxo uguna in aragti u dhigma.

set Compact ama CD - hoosaad ka mid ah meel topological, kaas oo la laaluusheen by nooca meel is haysta.

Xad is haysta (precompact) ayaa lagu wadaa kaliya in ay dhacdo circuit ah ee isafgaradka. Marka qoondaynta bannaan ee subsequence a is-waxaa loo yeedhi karaa sequentially is haysta.

set Compact wuxuu leeyahay sifooyin gaar ah:

- hab is haysta wax bandhigay joogto ah;

- hoosaad xiran mar walba is haysta a,

- bijection joogto ah, kaas oo lagu qeexay on is haysta a waxaa loola jeedaa homeomorphism.

Tusaalooyinka set dheggan yihiin:

- koobnayn oo xiray nooc RN,

- subsets uguna meelaha u dhigma cadayn ee T1 qeybinta;

- Aragtida Ascoli Arzela sifeeyay set is haysta ee boosaska functional gaar ah;

- meel Stone tirsan algebra ku Boolean;

- compactification of meel topological.

La tixgaliyo booska set universal leh xisaabta, mid ku doodi karaa in tani ay tahay go'an oo ka kooban hannaanka ka mid ah xubno la guryaha gaarka ah. Oo ay la socdaan set kale khiyaali ah waxaa ka mid ah qaybaha kala duwan ka wada hadleen fikradda jira. Si kastaba ha ahaatee, hantida lid ku ah nuxurka aad ee la ballamay.

In berrinkii set universal hoose xisaabta waxaa wakiil u ah abyoonayaasha. Si kastaba ha ahaatee, kaalin gaar ah iska leh set this ee aragtida set.

set ee abyoonayaasha ka mid ah set oo ah cunsur (tiro) waxaa laga yaabaa in kac si dabiici ah inta lagu guda jiro tirinta. Waxaa jira laba siyaabood ee go'aaminta tirada dabiiciga ah:

- wareejinta alaabta (koowaad, labaad, iwm);

- Tirada maadooyinka (mid ka mid ah, laba, iwm).

Xaaladdan oo kale, kala duwan oo aan abyoonayaasha iyo abyoonayaasha taban nooca dabiiciga ah ee tirada ma khuseeyaan. In berrinka xisaabeed ee la ballamay ee tirooyinka caadiga ah waa N. fikirka Tani waa dhammaadka lahayn, in joogitaanka tiro ka mid ah noocyada kale ee tirada dabiiciga ah dabiiciga ah kuwii hore ka badan ka sii weyn mahad.

Si ka duwan oo dabiici ah, tiro idil waxaa laga heli by hirgelinta hawlaha xisaabta on tirada dabiiciga ah sida Intaa waxaa dheer ama goynta. set ee abyoonayaasha xisaabta waxaa loo qoondeeyey Z. By kalagoynta natiijada isugaynta iyo kala-dhufashada laba tiro oo waa tirada nooc ka mid ah oo kaliya of nooca la mid ah. Baahida loo qabo noocan ah tirada dhacdo sabab la'aanta ah ee awooda si loo ogaado farqiga u dhexeeya laba abyoonayaasha. Waa Michael Stifel baro xisaabta tiro taban.

Waxay u baahan tahay taxader leh uga fikirtaan fikradaha sida meel bannaan oo is haysta. Ereygan waxaa soo bandhigay PS Alexandrov in la xoojiyo fikradda ah ee meel bannaan ah oo is haysta waa la soo bandhigay gelin xisaabta Frechet. faham buuxa ee nooca topological meel is haysta ay dhacdo subcovering uguna ded kasta u furan. In horumarka ku xiga ee xisaabta, compactness muddada noqday amar of magnitude ka badan ay dhigiisa hoose. Haddaba waxaa la fahamsan yahay by compactness compactness ah, iyo dareenka jirka muddada waa in horyaalka ah "countably is haysta." Si kastaba ha ahaatee, labada fikradaha waa u dhiganta marka loo isticmaalo meelaha ton.